In this paper, we present a wireless ECG-derived Respiration Rate (RR) estimation using an autoencoder with a DCT Layer. The wireless wearable system records the ECG data of the subject and the respiration rate is determined from the variations in the baseline level of the ECG data. A straightforward Fourier analysis of the ECG data obtained using the wireless wearable system may lead to incorrect results due to uneven breathing. To improve the estimation precision, we propose a neural network that uses a novel Discrete Cosine Transform (DCT) layer to denoise and decorrelates the data. The DCT layer has trainable weights and soft-thresholds in the transform domain. In our dataset, we improve the Mean Squared Error (MSE) and Mean Absolute Error (MAE) of the Fourier analysis-based approach using our novel neural network with the DCT layer.